Results 1 to 2 of 2

Math Help - Vector Calculus: Flux and divergence theorem

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    2

    Unhappy Vector Calculus: Flux and divergence theorem

    1. Consider a cube with vertices at A=(0,0,0) B=(2,0,0) C=(2,2,0) D=(0,2,0) E=(0,0,2) F=(2,0,2) G=(2,2,2) H=(0,2,2)
    A)Calculate the flux of the vector fieldF=xi through each face of the cube by taking the normal vectors pointing outwards.
    B)Verify Gauss's divergence theorem for the cube and the vector field F by computing each side of the formula.
    C)Using Gauss's divergence theorem evaluate the flux \int \int  F.dS of the vector field F=xi+yj+ z^2k where S is a closed surface consisting of the cylinder x^2 + y^2 = a^2, 0<z<b and the circular disks x^2 + y^2 , a^2 at z=0 and x^2 + y^2 = a^2 at z=b.

    I have the basics but dont know how to get an answer. My workings are attatched.
    Attached Thumbnails Attached Thumbnails Vector Calculus: Flux and divergence theorem-img.jpg  
    Last edited by bobmarley909; May 19th 2010 at 01:28 PM. Reason: maths editing
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Quote Originally Posted by bobmarley909 View Post
    1. Consider a cube with vertices at A=(0,0,0) B=(2,0,0) C=(2,2,0) D=(0,2,0) E=(0,0,2) F=(2,0,2) G=(2,2,2) H=(0,2,2)
    A)Calculate the flux of the vector fieldF=xi through each face of the cube by taking the normal vectors pointing outwards.
    B)Verify Gauss's divergence theorem for the cube and the vector field F by computing each side of the formula.
    C)Using Gauss's divergence theorem evaluate the flux \int \int F.dS of the vector field F=xi+yj+ z^2k where S is a closed surface consisting of the cylinder x^2 + y^2 = a^2, 0<z<b and the circular disks x^2 + y^2 , a^2 at z=0 and x^2 + y^2 = a^2 at z=b.

    I have the basics but dont know how to get an answer. My workings are attatched.

    z= 0 ,n= -k ,F ^. n = 0

    z = 2, n= k, F^.n =0

    y = 0, n= -j, F^.n = 0

    y = 2, n=j, F^. n = 0

    x=0, n=-i, F^. n = 0

    x = 2, n = i, F^. n =2

    So now

    \int^{2}_{0} \int^{2}_{0} 2 dxdy = 8

    Using divergence theorem

    \int^{2}_{0} \int^{2}_{0}\int^{2}_{0} dxdydz = 8

    c)

    \int^{2\pi}_{0} \int^{a}_{0} \int^{b}_{0} (2 +2z)r dzdrd\theta
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: May 7th 2011, 06:35 AM
  2. Replies: 3
    Last Post: August 30th 2010, 04:06 AM
  3. Vector calculus: divergence theorem! help!
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 11th 2010, 08:57 AM
  4. Divergence Theorem and Flux
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 9th 2010, 07:40 AM
  5. Replies: 2
    Last Post: April 3rd 2010, 04:41 PM

Search Tags


/mathhelpforum @mathhelpforum